Parallel plate conductors question

1. The problem statement, all variables and given/known data
"An electron is fired from a negative plate towards a hole in a positive plate. It then passes between two parallel plates that are 3 cm long and 2 cm apart with a voltage of 550 volts across them. If the accelerating voltage across the two original plates is 900 volts what is the final velocity of the electron?"

2. Relevant equations
ε = ΔV/d
ε = Fe/q

3. The attempt at a solution
I used the above equations to calculate the constant force on the electron by each electric field (since electric fields between parallel plates are constant, so is the electric force on the electron). I then divided that by the mass of the electron to find the constant acceleration in the x and y directions. Using the kinematics equation s = (aΔt^2)/2, I calculated the time it would take to go from one plate to the other in both electric fields, and found that the time to travel between the second set of parallel plates is shorter. Taking this time as the total time of travel, I multiplied the previously found accelerations in the x and y direction by this time of travel to obtain the x and y components of the final velocity. I then used the Pythagorean theorem and the tangent ratio to get the magnitude and direction of the final velocity.